How it works
A discount reduces the price by a percentage of that price. With two stacked discounts, each one applies to the already-reduced price — the second discount is not applied to the original, which is why the math is multiplicative, not additive.
Sale price = original × (1 − discount1%) × (1 − discount2%)
or if no second discount:
Sale price = original × (1 − discount1%)
Savings = original − sale price
Effective discount % = (1 − (sale price ÷ original)) × 100
Worked examples
Two scenarios showing why stacking discounts is not the same as adding them.
- Original price: $80.
- Apply 25% discount: $80 × (1 − 0.25) = $80 × 0.75.
- Sale price: $60.
- Savings: $80 − $60 = $20.
- Original price: $150.
- Apply 20% discount: $150 × 0.80 = $120.
- Apply 10% discount to the already-reduced price: $120 × 0.90 = $108.
- Sale price: $108 (same as $150 × 0.80 × 0.90).
- Savings: $150 − $108 = $42.
- Effective discount: (1 − $108/$150) = 1 − 0.72 = 0.28 = 28% — not 30%, even though 20 + 10 = 30. The gap grows with more stacked discounts.
Common questions
Why don't two stacked discounts just add together?
Because the second discount applies to the already-reduced price, not the original — 20% off then 10% off is 0.80 × 0.90 = 0.72, i.e. 28% off total, not 30%. The gap grows the more discounts are stacked.
What's the difference between markup and discount?
A discount reduces a price by a percentage of that price (original × (1 − discount%)). Markup increases a cost by a percentage to set a selling price — they're inverse operations, and this site's Markup Calculator handles that direction.
How do I find the original price from a sale price?
Divide the sale price by (1 − discount%) instead of multiplying. For example, a $60 sale price after 25% off means the original was 60 ÷ 0.75 = $80 — this calculator works forward (original → sale), not backward.